Question

A transverse wave on a string is described by the following wave function.
y = 0.080 sin(π/10x + 5πt)

where x and y are in meters and t is in seconds.

a) Determine the transverse speed at t = 0.210 s for an element of the string located at x = 1.80 m.

b) Determine the transverse acceleration at t = 0.210 s for an element of the string located at x = 1.80 m.

c) What is the wavelength of this wave?

d) What is the period of this wave?

e) What is the speed of propagation of this wave?

Answer 1

The easy stuff first:

\( \omega=5\pi\): The angular frequency
\(\large T={2\pi\over\omega}\) : The period
\(k=\dfrac \pi {10}\): The wave number
\(\large \lambda=\large {2\pi\over k}\): The wavelength
\(\nu=\large { \lambda \over T}\) or \(\nu=\large { \omega \over k}\): The speed of Propagation

To determine the transverse velocity and acceleration, we need to find \(\dfrac {dy}{dx}\) and \(\dfrac {d^2y}{dx^2}\) and then substitute the values for t and x that are given.

Hope this helped.

Good luck.